Lyapunov's First Theorem

Lyapunov's first theorem states that all the eigenvalues of an real matrix have negative real parts iff the Lyapunov equation

has a symmetric positive definite matrix solution , where is the identity matrix. Thus is a positive definite quadratic form.

See also

Lyapunov Equation, Lyapunov's Second Theorem

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References

Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, p. 1122, 2000.

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Lyapunov's First Theorem

Cite this as:

Weisstein, Eric W. "Lyapunov's First Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LyapunovsFirstTheorem.html

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